I have an entire personal thesis regarding time travel and it's potential in story writing. If you're interested I'll tell you more about it, but it is quite lengthy. I'll leave a summary below:
Types of Time Travel:
Traditional - if we consider the mainstream time travel as seen in most movies or as defined by the Time Machine by HG Wells. PROs - allows experiencing different time periods (past and future). CONs - you will be burdened by explaining and resolving paradoxes (which honestly is not worth the trouble as the pay-off is most often meh).
Time Control - moving time forward and backward in small increments as seen in the game Life is Strange and the Time Stone in Marvel Comics. This is a relatively simple method of time travel with minimal damage to time-space continuum. Technically, this happens all the time (especially in physics)
Time leap- jumping forward in time. This is also a relatively simple way of time travel. It's basically the same as suspended animation, just more instantaneous. Since this does not mess with time-space consistency and merely a displacement, there won't be paradoxes.
Dimension hop - travel to the present time in an alternate timeline (think Rick and Morty and the infinite Ricks and Mortys)
Now let us combine all of the above to make a more coherent scenario on how time travel can be possible without the drawbacks.
I call this my Overly Complicated Derivatively Acceptable Time Travel Theory.
First let us postulate that time travels in a straight line and assign this along the x-axis (x,0) let us call this the origin, now consider the chaos theory and assume that each possibility (each potential random result) generates it's own timeline that runs parallel the axis. Now consider their position away from the origin (x,y), the farther away they from the origin (positive or negative), the greater the difference/deviance from the original timeline.
Second, let us consider a wave passing through these lines originating from any point along (x,0) with an amplitude=infinity. This wave represents the start of consciousness and each time the wave intersects the origin this represents a turning point in history. The area between these points is what I consider the central finite curve (from Rick and Morty) where all possible decisions will result in the same major turning point. i.e. if Germany didn't start WWII, someone else would have.
Third, consider time travel as a function of arctan originating from one timeline and terminates parallel to another.
If we consider these three assumptions, preservation of matter, and interdimensional displacement, there would be a few ways to accomplish time travel back to the past. In a perspective of one character, we can consider the transfer of consciousness. This means, you transfer your current consciousness to your past self arming yourself with knowledge of the future. An interesting point to this is that the possibility already exists with or without you travelling back in time.
Travelling to the past where you entirely do not exist is a different matter. In my theory, this would require a great amount of energy and expectedly a machine from which to draw and convert this energy. This is a must keep readers engaged, otherwise your character would just plainly be OP if they can travel forward and back by themselves with no repercussions. Individuals with this kind of ability are usually restrained by rules and are not usually meant to be the driving force in a story
TL;DR if you will consider to have time travel as a driving force in your story, make it coherent and plausible via a gimmick. A good example can be seen in Umbrella Academy, Number 5 can time travel but the way to do it is complicated, they have a gimmick where a secret organization uses special briefcases that allow time travel into the past. In your idea, where the hero is leaving behind his original galaxy/dimension is all well and good. It is justifiable in a proper space-time continuum sense. Creating duplicate galaxies however, is kind of a stretch. I mean, could you imagine how much energy would be required to do such a thing? Also, there is an issue with duplicating galaxies as they are visible via telescope and discovering that their is a galaxy identical to theirs (although is a good plot point) may be hard to explain.